MONTPELIER — In the nick of time to help solve an eleventh-hour budgetary dilemma, the Shumlin administration arrived at the Statehouse Wednesday with millions of dollars in new savings.

On Tuesday, lawmakers and Gov. Peter Shumlin cut a budget deal that will require them to trim $10 million from the fiscal year 2014 spending plan.

On Wednesday, Administration Secretary Jeb Spaulding got them nearly halfway there with a proposal for “overtime reduction and management strategies” and “enhanced revenue collections.”

“We’re always looking for ways to improve our management,” Spaulding said. “And when we look at the options we have out there, we’re going to have to work harder.”

House Minority Leader Don Turner said the timing of the proposals makes him skeptical. He said the savings plan lacks any specificity, and appears to paper over a budgetary problem that Democratic officials don’t have the stomach to resolve with more substantive cuts.

“If we can save $2.5 million from reduced overtime and improved management, shouldn’t we be doing that already?” Turner asked. “And enhanced revenue collection? It seems like a convenient time for these solutions to suddenly arise.”

Spaulding said he appreciates Turner’s skepticism. The new savings plan had been absent from the first four months of the legislative session, and materialized less than 24 hours after the deal opened up a $10 million hole in next year’s budget.

“But I want to make it clear: it’s not funny money,” Spaulding said.

“We think we can generate those savings,” Spaulding said. “The governor has been clear about not raising taxes. And in order for the administration to do its part to not raise taxes, we’re going to have to dig deeper.”

The $2.5 million in administrative savings and $1.5 million that would be generated by more aggressive revenue collection strategies are the biggest line items in a $6.2 million savings plan agreed to by House and Senate lawmakers Wednesday.

Except for an $850,000 reduction to a reserve fund, that plan avoids cuts altogether, and relies instead on reductions in spending projections to offset the $10 milion gap.

Among those spending reductions: The administration learned recently that it will owe about $1 million less on Medicare payments to the federal government next year, and about $225,000 less on interest payments on its unemployment loan.

Sen. Jane Kitchel, a Caledonia County Democrat and chairwoman of the Senate Committee on Appropriations, said she has full confidence in the administration’s projections.

“We asked that question: are these achievable?” Kitchel said. “Don’t forget we’re talking about a $1.3 billion (general fund) here. And our view is that the savings are achievable.”

Spaulding will return to the Statehouse today with proposals for additional reductions. While lawmakers and the administration have yet to tap the $8 million in projected surplus funds theoretically at their disposal, it’s possible they’ll preserve those dollars to fund a reserve heading into the next fiscal year.

That could make finding the last $4 million in savings more difficult than getting the first $6 million proved to be.

Turner said he worries the House and Senate are simply avoiding the tough budget cuts that their decision not to raise new taxes should have forced them into now.

“I’m concerned that we’re going to come back here next January with a budget adjustment request for all the savings they’re booking now that didn’t get accomplished.”